Thank you. Seeing your reply, I remembered more. The phrase was 「二人が対面した時に…」 If the subject were two people as in the example, does the 面会した suggest that they met/visited a third person and 対面した was a meeting between them two?
– macrafSep 8 '15 at 10:50

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「会った」is the most general way to say "meet." So, if this is not used, there should be a slight difference. 「二人が対面した時に…」means "When two faced each other,". In my opinion, the two should concentrate on each other, and it is ok to use it even when there is a third person, but the speaker does not care about them. I found something like「不仲の噂される Messi と Ronaldo がサッカーの試合直前に対面したが、談笑していた。(They say Messi and Ronaldo hate each other, but they face just before the game and talked cheerfully.)」on web.
– Keita ODASep 12 '15 at 21:03

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「二人が面会した時に…」means "When two met,". In my opinion, 面会 requires some processes like a reservation or an approval. And, I said "sometimes used to ... in a hospital or in a prison", but I should say mostly. I searched it on web and the first page was made of a dictionary, a court and hospitals. kotobank.jp/word/%E9%9D%A2%E4%BC%9A-644517 According to デジタル大辞泉, 面会: meet a special person or meet in a special place. 対面: often used when they first meet or after a long time no see. 面接: Meet personally to ask questions. I think they point out good points.
– Keita ODASep 12 '15 at 21:15